Separating Solution of a Quadratic Recurrent Equation

In this paper we consider the recurrent equation for p ≥1 with f ∈ C [0,1] and Λ 1 = y >0 given. We give conditions on f that guarantee the existence of y (0) such that the sequence Λ p with Λ 1 = y (0) tends to a finite positive limit as p →∞.

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Bibliographic Details
Published inJournal of statistical physics Vol. 136; no. 4; pp. 603 - 613
Main Authors Sinai, Y. G., Vinogradov, I.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.08.2009
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Separating solution
Quadratic recurrent equation
Mellin transform
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Summary:In this paper we consider the recurrent equation for p ≥1 with f ∈ C [0,1] and Λ 1 = y >0 given. We give conditions on f that guarantee the existence of y (0) such that the sequence Λ p with Λ 1 = y (0) tends to a finite positive limit as p →∞.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-009-9801-6